One of this year's biggest winners in currency markets, the New Zealand dollar, has turned into one of its biggest losers.

The currency, nicknamed the kiwi, dropped 3.8% against the U.S. dollar since its 2014 peak on July 9, making it the worst performer among the 10 most-traded currencies over that period and wiping out more than half of this year's gains.

The dairy-dependent economy has been whacked by falling milk prices,...